Mathematical cognition provides a foundation for the development of skills that are indispensable for academic and professional success in the 21st century. Strong foundational knowledge in math is critical not only for success in the STEM fields but also as an important skill in everyday life. Poor numeracy is associated with negative and costly outcomes for health, well-being and life expectancy, making it a major public health concern. Mathematical difficulties are widespread in children, adolescents and even college students, and one in five adults in the US is functionally innumerate. Interventions for remediating poor math skills in children with mathematical disabilities (MD) have therefore taken on great significance. The long-term goal of our research is to understand the cognitive and brain mechanisms underlying mathematical learning, and remediation of poor math skills, in children with MD. Research into the mechanisms underlying interventions for assisting students struggling with math is critically needed, as emphasized by multiple expert panels. Our proposal seeks to extend a productive, innovative and high-impact line of research using a cognitive and systems neuroscience approach, together with state-of-the-art brain imaging techniques, to examine the mechanisms underlying remediation of mathematical skills in children with MD. Our proposed studies are highly relevant to the mission of the NIH Program Announcement Development of Mathematical Cognition and Reasoning and the Prevention of Math Learning Disabilities (PA-12-248). Building on our recent progress, in this renewal we now propose to investigate the cognitive and brain mechanisms underlying two important types of interventions that target different areas of weaknesses in children with MD - speeded practice tutoring (SPT), which targets fluent retrieval of math facts, and visuo-spatial number tutoring (VNT), which targets visuo-spatial representations of numbers, quantity, and their mental manipulations. We will use a randomized control design to compare these distinct learning approaches, and elucidate the brain mechanisms underlying short- and long-term learning, generalization (transfer), and retention of math skills associated with SPT and VNT in children with MD. Our central hypothesis is that SPT and VNT will remediate different types of math deficits in children with MD via dissociable patterns of brain plasticity. A critical neurobiological investigation of these two forms of learning will help elucidate the extent to which MD is remediated by interventions that target plasticity in dissociable brain systems - the declarative memory system, anchored in the medial temporal lobe and the visuo-spatial attention system, anchored in the intra- parietal sulcus. The proposed work will provide important new insights into the neurobiological basis of mathematical learning in children with MD and their typically developing peers. Findings from our study have major implications not only for informing the etiology and the remediation of MD but also for determining sources of variability in mathematical learning with broad consequences for optimizing learning in all children.